Admission Control Algorithms for Revenue Optimization with QoS Guarantees in Mobile Wireless Networks Authors: I.R. Chen, O. Yilmaz and I.L. Yen Presented By: Rose Njeck, David Jones, & Kenneth Nehring

Agenda Introduction System Model Mobility & Service Call Pattern Admission Control for Revenue Optimization with QoS Guarantees  Partitioning Admission Control  Threshold-Based Admission Control  Hybrid Partitioning and Threshold-Based Admission Control Numeric Data & Analysis Applicability and Summary

Introduction Next generation wireless networks  Real-time multimedia: video and audio  Non-real-time services: images and files Requires network that easily adapts to  User needs  Growing population  Without compromising Quality of Service (QoS) Two of the most important QoS measures in cellular networks: percentage of new and handoff calls blocked due to channel unavailability

Introduction Establish communication with base station Base station supports limited number of connections Handoff occurs when mobile user with ongoing connection enters new cell Connection may be dropped during handoff Reduce handoff call drop probability by rejecting new connection requests, but results in increase of new call blocking probability Tradeoff between handoff and new call blocking probabilities

Introduction Partition, threshold-based and hybrid admission control algorithms make acceptance/rejection decisions based on  Satisfying QoS requirements  Optimizing revenue Achieved by integrating pricing with call admission control Assume static “charge-by-time” pricing algorithm

Introduction Definitions  Partitioning: number of channels are reserved to serve handoff (or new) calls of a service type  Threshold-based: handoff (or new) calls of a service type are given an admission threshold

System Model Cellular Network as flat architecture: cells connected consecutively Base station at the center of each cells that provides services to mobile hosts within the cell Distinct number of service classes characterized by their type attribute:  Real-time services  Non real-time services

System Model Each service type has  Handoff calls with higher priority  New calls  Might impose system wide QoS requirement Each service class i has a QoS constraint on B i ht and on B i nt

System Model- single cell perspective Service class characteristics i n – Arrival rate of new calls of service class i  i n – Departure rate of new calls of service class i i h – Arrival rate of handoff calls of service class i  i h – Departure rate of handoff calls of service class i Cell has C channel  C depends on the available bandwidth Service call of class i requires k i channels

System Model – service provider perspective each cell makes admission control decisions for new and handoff call requests taking into consideration of the price rate information of these service calls in order to maximize the revenue received from servicing new and handoff calls in the cell. Price-rate scheme adopted:  Calls of service class i have a charge rate of v i per time unit

Mobility & Service Call Patterns Need a way to estimate: i n – Arrival rate of new calls of service class i  i n – Departure rate of new calls of service class i i h – Arrival rate of handoff calls of service class i  i h – Departure rate of handoff calls of service class i i n i h inin inin Mobility and service call patterns are used by cells in a wireless network to make admission control decisions to allocate resources to calls. Requires each mobile user to intelligently know their expected arrival and departure rate for the current cell they occupy. Need a mechanism to estimate these rates.

Mobility & Service Call Patterns Mobility & service call pattern recognition algorithm executed on individual mobile devices  Helps to achieve scalability Two data structures stored on mobile devices to summarize the data computed from the algorithm  Mobility Probability Matrix  Service Call Table

Mobility Probability Matrix Summarizes the probability (P BCD ) of the mobile user going from one cell to the next cell and the residence time (T BCD ) of each cell, given that the mobile user comes from a previous cell. BCD P BCD T BCD A Including Cell A Introduces a trade-off between storage and processing requirements for accuracy You are here

Mobility Probability Matrix To calculate probabilities, reward correct state transitions and penalize incorrect ones. The sum of all probabilities is one. D1D1 D6D6 D2D2 D5D5 D3D3 D4D4 C P BCD1 P BCD2 P BCD3 P BCD4 P BCD5 P BCD6 Before Transition Transition To D 3 With a transition to D 3, P BCD3 is rewarded 10% while the rest are penalized 2% C can go to D 1 through D 6

Mobility Probability Matrix For mobile users that exhibits a certain degree of regularity for movements and calls, the matrix will eventually concentrate on certain state transition probabilities with values close to 1. The matrix will summarize the regular paths taken by the mobile user. T BCD1, T BCD2, T BCD3, T BCD4, T BCD5, and T BCD6 are updated accordingly depending on the actual path taken by the mobile user. Values are easily determined by keeping track of the average dwell time that the mobile user stays in a particular cell, given the history of the previous cell and the next cell. Average Dwell Time

Service Call Table Maintained by individual mobile devices to summarize call patterns. Populated as the mobile device goes through a sequence of calls. Stores four “rate” values for each cell visited by a mobile device. Rate Values Stored:  n (C) – Arrival rate of a new call made in cell “C”  n (C) – Departure rate of a new call from cell “C”  h (C) – Arrival rate of a handoff call from cell “C” into its neighbor cells  h (C) – Departure rate of a terminated handoff call from cell “C” C  n (C)  h (C)  n (C)

Arrival & Departure Rates for a Cell Arrival rate of handoff calls for cell “C” B1B1 C  h (B)xP BC B2B2 B3B3 BMBM  h (B) = Arrival rate of a handoff call from cell “B” into its neighbors M = set of neighbor cells of cell C (From Probability Matrix)

Arrival & Departure Rates for a Cell Arrival rate of new calls for cell “C” Departure rate of new calls for cell “C” Departure rate of handoff calls for cell “C” Note that the arrival rate of all new calls is an aggregate measure summing all new call arrival rates by individual users in the cell, while the departure rate per call is an average parameter, averaging over all the mobile users in the cell.

Admission Control for Revenue Optimization with QoS Guarantes Partitioning Admission Control Threshold-Based Admission Control Hybrid Admission Control Assume two service types  class 1 (high-priority) 1 n,  1 n, 1 h, and  1 h  class 2 (low-priority) 2 n,  2 n, 2 h, and  2 h

Partitioning Admission Control A partitioning call admission control policy divides the total number of channels in a cell into several fixed partitions with each partition specifically reserved to serve a particular service class (real-time vs. non-real-time) and call type (new vs. handoff). C 1 h, C 1 n, C 2 h, C 2 n ≤ C > C 1 h + C 1 n + C 2 h + C 2 n = C

Partitioning Admission Control Channels in a partition cannot be shared. If a new high-priority (i.e. class 1) call arrives at a cell and all channels allocated to serve high- priority new calls are used up, the call is rejected. This applies to all service classes and call types.  Like a M/M/n 1 n /n 1 n queue where n 1 n = number of call slots, with arrival rate 1 n and service rate  1 n.

Input Parameters to a Cell Arrival RatesDeparture RatesNumber of Channels Threshold Blocking Probabilities 1 h 1 n 2 h 2 n 1h1n2h2n1h1n2h2n Price Rates v1v2v1v2 k1k2k1k2 B1htB1ntB2htB2ntB1htB1ntB2htB2nt The following parameters are used by a cell’s admission control algorithm:

QoS Constraints A blocking probability is the probability a call is rejected. Blocking probabilities of new and handoff calls for both classes 1 and 2 must be satisfied. We would like to partition the channels such that the following QoS constraints are satisfied: B 1 h < B 1 h t B 1 n < B 1 n t B 2 h < B 2 h t B 2 n < B 2 n t The blocking probabilities can be easily determined by calculating the probability of the partition allocated to serve the specific calls being full.

Revenue Generation The revenue that a successfully terminated or handed-off call brings to the cell is calculated by the product of the call’s price rate parameter v i with the duration of the call in the cell. Under partitioning, a cell will receive the following revenue per time unit: N 1 h = Number of high-priority handoff. calls in the cell N 1 n = Number of high-priority new calls. in the cell N 2 h = Number of low-priority handoff. calls in the cell N 1 n = Number of low-priority new calls. in the cell

Revenue Generation The revenue rate earned by the partitioning algorithm is as follows: PR(C, 1 h, 1 n, 2 h, 2 n ) = PR 1 h + PR 1 n + PR 2 h + PR 2 n PR 1 h, PR 1 n, PR 2 h, and PR 2 n stand for the revenues generated per unit time due to high-priority handoff calls, high-priority new calls, low-priority handoff calls, and low-priority new calls respectively.

Revenue Optimization Need to identify the best partition sizes (C 1 h, C 1 n, C 2 h, C 2 n ) that will maximize the cell’s revenue subject to the imposed QoS constraints.

Threshold-Based Admission Control C 1 h >= C T, C 1 n >= C T > C 2 h ≤ C T,C 2 n ≤ C T

Threshold-Based Admission Control SPN Model

Threshold-Based Admission Control SPN Model E i h – models handoff call arrivals of service class i at rate λ i h E i n – models new call arrivals of service class i at rate λ i n S i h – models service of handoff call arrivals of service class i with a service rate of M(UC i h ) multiplied with μ i h where M(UC i h ) stands for the number of tokens in place UC i h S i n – models service of new call arrivals of service class i with a service rate of M(UC i n ) multiplied with μ i n where M(UC i n ) stands for the number of tokens in place UC i n UC i n – models the execution state of service class i new calls UCi h – models the execution state of service class i handoff calls

Threshold-Based Admission Control A new service request arrival is admitted only if the threshold assigned is not yet reached.   Assign an enabling predicate to guard E i n, E i h with thresholds C i n and C i h

Threshold-Based Admission Control Enabling predicate of E 1 n M(UC 1 n ) + M(UC 1 h )] k 1 + k 1 + [M(UC 2 n ) + M(UC 2 h )] k 2 ≤ C 1 n Enabling predicate of E 1 h is [M(UC 1 n ) + M(UC 1 h )] k 1 + k 1 + [M(UC 2 n ) + M(UC 2 h )] k 2 ≤ C 1 h Enabling predicate of E 2 n is [M(UC 1 n ) + M(UC 1 h )] k 1 + k 2 + [M(UC 2 n ) + M(UC 2 h )] k 2 ≤ C 2 n Enabling predicate of E 2 h is [M(UC 1 n ) +M(UC 1 h )] k 1 + k 2 + [M(UC 2 n ) + M(UC 2 h )] k 2 ≤ C 2 h

Threshold-Based Admission Control SPN Model- Blocking probabilities where rate(E i c ) is calculated by finding the expected value of a random variable X defined as X= λ i c if E i c is enabled and 0 otherwise

Revenue Generation The revenue generated per unit time from the threshold-based admission control algorithm to the cell is defined by: Where TR 1 h, TR 1 n, TR 2 h, and TR 2 n stand for the revenues generated per unit time due to high-priority handoff calls, high-priority new calls, low- priority handoff calls, and low-priority new calls, respectively, given by:

Hybrid Admission Control The hybrid algorithm divides the channels into fixed partitions the same way partitioning algorithm does. In addition, a “shared” partition is reserved to allow calls of all service classes to compete for usage in accordance to threshold algorithm. n 1 hs k 1 + n 1 ns k 1 + n 2 hs k 2 + n 2 ns k 2 ≤ C s Constraints C 1 h + C 1 n + C 2 h + C 2 n + C s = C

Hybrid Admission Control The shared partition is available for use by a service class only if the partition reserved for that service class is used up. QoS constraints and revenue earned per unit time remain applicable B 1 h < B 1 h t B 1 n < B 1 n t B 2 h < B 2 h t B 2 n < B 2 n t

Hybrid Performance Model Hybrid algorithm encompasses algorithms as special cases  Partitioning: C s =0  Threshold-based: C 1 h, C 1 n, C 2 h, C 2 n all equal 0 Hybrid performance model composed of two submodels  Partitioning: C 1 h, C 1 n, C 2 h, C 2 n  Threshold-based: C=C s

Hybrid Performance Model Shared partition arrival rates  Arrival rate is the sum of spill over rates from each fixed partition (modeled as M/M/n/n queues) Arrival rates into shared partition λ 1 hs = high priority handoff calls λ 1 ns = high priority new calls λ 2 hs = low priority handoff calls λ 2 ns = low priority new calls Similar expressions for λ 1 ns, λ 2 hs, and λ 2 ns Erlang’s B formula

Hybrid Revenue Generation Revenue generated per unit time from hybrid admission control algorithm is sum of revenues earned from the fixed partitions plus that earned from the shared partition HR(C, λ 1 h, λ 1 n, λ 2 h, λ 2 n ) = PR(C-C s, λ 1 h, λ 1 n, λ 2 h, λ 2 n ) + TR(C s, λ 1 hs, λ 1 ns, λ 2 hs, λ 2 ns ) Optimization for hybrid admission control algorithm: Identify the best partition (C 1 h, C 1 n, C 2 h, C 2 n, C s ) to maximize the revenue subject to imposed QoS constraints

Numeric Data and Analysis Results include partitioning, threshold-based and hybrid admission control algorithms for revenue optimization with QoS guarantees Charging rate model based on popular “charge- by-time” scheme Two classes of service  Class 1 (real-time): demands more resources and higher QoS  Class 2 (non-real-time)

Algorithm Comparisons, λ 1 h An increase in revenue/time equals $$$ 1 h PartitioningHybridThreshold-based (C 1 h, C 1 n, C 2 h, C 2 n )Revenue/Time(C 1 h,C 1 n,C 2 h, C 2 n, C s )Revenue/Time(C 1 hT,C 1 nT, C 2 hT, C 2 nT )Revenue/Time 1(16,56,4,4) (8, 72,0,0,36) (80,80,80,80) (20,52,4,4) (12,36,0,0,32) (80,80,80,80) (20,52,4,4) (12,32,0,0,36) (80,80,80,80) (28,44,4,4) (16,32,0,0,32) (80,80,80,80) (32,40,4,4) (16,32,0,0,32) (80,80,80,80) (32,40,4,4) (16,28,0,0,36) (80,80,76,76) None (16,28,0,0,36) (80,80,76,76) None (20,24,0,0,36) (80,80,76,76) None (20,24,0,0,36) (80,80,76,76) None (20,24,0,0,36) (80,80,76,76) None (20,20,0,0,40) (80,80,76,76) None (20,20,0,0,40) (80,76,75,72) None (24,20,0,0,36) None 7.5None (24,20,0,0,36) None C=80,  1 h = 1.0, 1 n = 6.0,  1 n = 1.0, 2 h = 1.0,  2 h = 1.0, 2 n = 1.0,  2 n = 1.0, v 1 = 80, v 2 = 10, k 1 = 4, k 2 = 1, B 1 h t = 0.02, B 2 h t = 0.04, B 1 n t = 0.05, B 2 n t = 0.1.

Analysis, λ 1 h As λ 1 h increases, the revenue rate obtainable also increases as long as QoS constraints can still be satisfied given the amount of resources available As λ 1 h increases further past a threshold value, all algorithms eventually fail to yield a solution because workload is too heavy to satisfy the imposed QoS constraints The hybrid admission control is the most tolerant among all in terms of being able to yield a solution under high workload situations

Analysis, λ 1 h Superiority of hybrid admission control over partitioning and threshold-based admission control due to  Ability to optimally reserve dedicated resources for high-priority classes through fixed partitioning to reduce interference from low-priority classes  Ability to optimally allocate resources to the shared partition in accordance with threshold-based admission control to exploit the multiplexing power for all classes

Algorithm Comparisons, λ 2 h & λ 2 n 2 h & 2 n PartitioningHybridThreshold-based (C 1 h, C 1 n, C 2 h, C 2 n )Revenue/Time(C 1 h,C 1 n,C 2 h, C 2 n, C s )Revenue/Time(C 1 hT,C 1 nT, C 2 hT, C 2 nT )Revenue/Time 1(48,24,4,4) (32,16,0,0,32) (80,80,80,80) (44,24,6,6) (28,12,0,0,40) (80,80,80,80) (44,20,8,8) (28,12,0,0,40) (80,80,80,80) (44,20,8,8) (28,12,1,1,38) (80,80,80,80) (40,20,10,10) (28,12,2,2,36) (80,80,80,80) (40,20,11,9) (24,8,2,2,44) (80,80,80,80) None (24,8,2,2,44) (80,80,80,80) None (24,8,3,3,42) (80,80,80,80) None (20,8,3,3,46) (80,80,76,76) None (20,8,3,3,46) (80,80,76,76) None (20,8,4,4,44) (80,80,76,76) None (20,4,3,3,50) (80,80,76,76) None (16,4,3,3,54) (80,80,76,76) None (16,4,3,3,54) (80,80,76,76) None (16,4,3,3,54) (80,80,76,76) None (16,4,6,6,48) (80,80,76,75) None (12,0,2,2,64) None C=80, 1 h = 5.0,  1 h = 1.0, 1 n = 2.0,  1 n = 1.0,  2 h = 1.0,  2 n = 1.0, v 1 = 80, v 2 = 10, k 1 = 4, k 2 = 1, B 1 h t = 0.02, B 2 h t = 0.04, B 1 n t = 0.05, B 2 n t = 0.1.

Analysis, λ 2 h & λ 2 n As the arrival rate of low-priority class increases, hybrid admission control  Decreases the number of dedicated channels allocated to high-priority calls  Increases the number of shared channels to exploit the multiplexing power in the shared partition  Attempts to allocate as much resources to low-priority calls as possible since the system will gain most of its revenue from low-priority calls Hybrid admission control performs the best over a wide range of arrival rate of low-priority calls

Algorithm Comparisons, v 1 :v 2 (v 2 =10) v 1 : v 2 PartitioningHybridThreshold-based (C 1 h, C 1 n, C 2 h, C 2 n )Revenue/Time(C 1 h,C 1 n,C 2 h, C 2 n, C s )Revenue/Time(C 1 hT,C 1 nT, C 2 hT, C 2 nT )Revenue/Time Low Class 1 Call Arrival Rates ( 1 h = 1.0, 1 n = 1.0) 1(20, 16, 22, 22) (12,12,5,5,46) (80,80,80,80) (20, 16, 22, 22) (12,12,5,5,46) (80,80,80,80) (20, 20, 20, 20) (16,12,5,5,42) (80,80,80,80) (20, 20, 20, 20) (16,12,5,5,42) (80,80,80,80) (20, 20, 20, 20) (16,16,7,5,36) (80,80,80,80) (20, 20, 20, 20) (16,16,7,5,36) (80,80,76,76) (24, 20, 18, 18) (16,16,7,5,36) (80,80,76,76) (24, 24, 16, 16) (16,16,7,5,36) (80,80,76,76) High Class 1 Call Arrival Rates ( 1 h = 3.5, 1 n = 4.5) 1None (8,12,5,5,50) (80,80,80,80) None (12,16,4,4,44) (80,80,80,80) None (12,16,3,3,46) (80,80,80,80) None (12,16,2,2,48) (80,80,76,76) None (12,16,1,1,50) (80,80,72,72) None (12,16,0,0,52) (80,80,72,69) None (12,16,0,0,52) (80,80,71,66) None (12,16,0,0,52) (80,80,71,66) C=80,  1 h = 1.0,  1 n = 1.0, 2 h = 10.0,  2 h = 1.0, 2 n = 10.0,  2 n = 1.0, v 2 = 10, k 1 = 4, k 2 = 1, B 1 h t = 0.02, B 2 h t = 0.04, B 2 n t = 0.05, B 2 n t = 0.1.

Analysis, v1:v2 (v 2 =10) Difference in revenue earned becomes more significant as the v1:v2 ratio increases Especially pronounced when system is heavily loaded under which it is necessary to optimally allocate channels to calls to maximize revenue and satisfy imposed QoS constraints Hybrid admission control either outperforms or is as good as partitioning and threshold-based admission control

Algorithm Comparisons, QoS (B 1 h t, B 2 h t) PartitioningHybridThreshold-based (C 1 h, C 1 n, C 2 h, C 2 n )Revenue/ Time(C 1 h,C 1 n,C 2 h, C 2 n, C s )Revenue/ Time(C 1 hT,C 1 nT, C 2 hT, C 2 nT )Revenue/ Time Low Class 1 Call Arrival Rates ( 1 h = 1.0, 1 n = 1.0) (0.02,0.04) x 2 0 (20,20,20,20) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -1 (20,20,20,20) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -2 (20,20,20,20) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -3 (24,20,20,20) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -4 (24,20,20,20) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -5 (24,20,21,19) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -6 (28,16,22,14) (16,12,5,5,42) (80,80,80,80) (0.02,0.04) x 2 -7 (28,16,23,13) (16,12,5,5,42) (80,80,80,80) …None … ……… (0.02,0.04) x None (16,12,5,5,42) (80,76,76,61) (0.02,0.04) x None (16,12,5,5,42) (80,76,76,54) (0.02,0.04) x None (16,12,5,5,42) (80,76,76,48) (0.02,0.04) x None (16,12,5,5,42) (80,76,76,42) (0.02,0.04) x None (16,12,5,5,42) None High Class 1 Call Arrival Rates ( 1 h = 3.5, 1 n = 4.5) (0.02,0.04) x 2 0 None (12,16,2,2,48) (80,80,76,76) (0.02,0.04) x 2 -1 None (12,16,2,2,48) (80,80,76,76) (0.02,0.04) x 2 -2 None (20,8,1,1,50) (80,76,76,76) C=80,  1 h = 1.0,  1 n = 1.0, 2 h = 10.0,  2 h = 1.0, 2 n = 10.0,  2 n = 1.0, v 1 = 80, v 2 = 10, k 1 = 4, k 2 = 1, B 1 n t=0.05, B 2 n t=0.1.

Analysis, QoS Under light-load conditions, all three algorithms can reasonably adapt to the QoS change Partitioning admission control generates relatively lower revenue because without multiplexing power, it needs to trade revenue off for QoS When QoS constraints of handoff calls becomes extremely tight, both partitioning and threshold-based admission control algorithms fail to provide solutions Hybrid admission is able to provide a solution due to its ability to exploit the multiplexing power in the shared partition and to reserve dedicated resources for individual service classes

Analysis, QoS Under heavy-load situations, hybrid admission control is more adaptable to stringent QoS constraints Hybrid admission control allocates more channels in  The C 1 h partition and conversely fewer channels in C 1 n to satisfy the most stringent QoS constraint imposed on class 1 handoff calls  The shared partition to satisfy stringent QoS requirement of class 2 handoff calls, which through multiplexing also has the benefit of compensating class 1 and class 2 new calls to satisfy QoS constraints The channel allocation made by hybrid admission control algorithm represents best possible way to satisfy varying QoS requirements while maximizing revenue earned

Summary Analyzed design concept for the integration of pricing with admission control algorithms with QoS guarantees in a cellular wireless network Admission control algorithm should consider not only QoS constraints imposed by system, but also the revenue that the admission of such a call will bring to the system when deciding which calls to admit Three admission control algorithms with intention of maximizing revenue generated by a cell while satisfying QoS constraints  Partitioning  Threshold-based  Hybrid admission control

Summary Using optimized conditions, the hybrid admission control algorithm can generate higher revenue with QoS guarantee than the other two admission control algorithms Attribute the superiority of the hybrid algorithm to  Existence of fixed partitions reserved for specific classes to avoid interference from other classes so as to satisfy the QoS requirements  Shared partition which provides great multiplexing power for sharing the bandwidth among calls of different classes

Applicability Cell dynamically communicates with mobile users in its cell and neighboring cells to obtain values or arrival and departure rates of new/handoff calls of various service classes Performs a simple table lookup at runtime to obtain the optimal (C h 1, C n 1, C h 2, C n 2, C s )

Future research Consider other pricing models and investigate optimal resource allocation settings Consider other revenue collection models  Revenue only collected on call termination  Revenue is lost when call terminated prematurely Explore relationship between QoS and pricing  Determine the optimal pricing for calls of various service classes  Such that revenue is maximized with QoS guarantees based on anticipated workload conditions and resource availability

Questions?